Cable-driven continuum robots with hyper-redundant deformable backbones show great promise in applications, such as inspection in unstructured environments, where traditional rigid robots with discrete links and joints fail to operate. However, the motion of existing continuum robots is still constrained by their homogeneous backbones, and limited to environments with modest geometrical complexity. In this study, inspired by highly deformable elephant trunks, we presented a modular tensegrity structure with preprogrammable stiffness for continuum robots. Then we derived a mechanical model based on a positional formulation finite element method for predicting the configuration of the structure in different deformation scenarios. Theoretical predictions revealed that the curvature of each segment could be regulated by preprogramming their spring stiffness. Hence, our customizable design could offer an effective route for efficient robotic interactions. We further fabricated a continuum robot consisting of 12 modules, and showcased its deformation patterns under multiple scenarios. By regulating the distribution of spring stiffness, our robot could move through channels with varying curvatures, exhibiting its potential for applications where varying curvature, and conformal and efficient interactions are needed. Leveraging the inherent intelligence, this robotic system could simplify the complexity of the required actuation and control systems.